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- W2971334013 abstract "Let $G$ be a simply connected Lie group with Lie algebra $mathfrak{g}$ and denote by $mathrm{C}_{bullet}(G)$ the DG Hopf algebra of smooth singular chains on $G$. In a companion paper it was shown that the category of sufficiently smooth modules over $mathrm{C}_{bullet}(G)$ is equivalent to the category of representations of $mathbb{T} mathfrak{g}$, the DG Lie algebra which is universal for the Cartan relations. In this paper we show that, if $G$ is compact, this equivalence of categories can be extended to an $mathsf{A}_{infty}$-quasi-equivalence of the corresponding DG categories. As an intermediate step we construct an $mathsf{A}_{infty}$-quasi-isomorphism between the Bott-Shulman-Stasheff DG algebra associated to $G$ and the DG algebra of Hochschild cochains on $mathrm{C}_{bullet}(G)$. The main ingredients in the proof are the Van Est map and Gugenheim's $mathsf{A}_{infty}$ version of De Rham's theorem." @default.
- W2971334013 created "2019-09-05" @default.
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- W2971334013 creator A5057310528 @default.
- W2971334013 date "2020-07-15" @default.
- W2971334013 modified "2023-09-25" @default.
- W2971334013 title "Singular chains on Lie groups and the Cartan relations II" @default.
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